Organ transplantation has come to be established as a sort of medical practice where no therapy is available other than organ replacement. In recent years, however, a currently increased number of organ transplant survival and a follow-up survey of transplant recipients, or the patients each having had an organ transplanted, reveal that there is arising the problem of greater concern in that the transplanted organs have been undergoing gradual fibrosis with an elapse of a prolonged period of time after the organ transplantation. In the organ transplantation, immunosuppressive drugs are used, for example, to suppress rejection of the transplanted grafts or the transplanted tissues, and must continue to be taken by the patients throughout their lifetime, except in the case of autografts or isografts. The fibrosis of a transplanted organ is found to develop in the graft-recipient patient who is kept placed on indefinite, continued immunosuppressant regimens. Although the causal relationship between the use of immunosuppressive drugs and the onset of the transplanted organ fibrosis is yet to be clarified, there has not been known so far any means to suppress the fibrosis of transplanted organs in the continued immunosuppressant regimens. It has heretofore been considered necessary for a patient to continue to take the immunosuppressive drugs throughout its lifetime, since such immunosuppressants are essential for the establishment and survival of grafts. Referring particularly to such immunosuppressive drugs, Cyclosporine and FK 506 (Taclolimus), with their potent immunosuppressive activity, have attained excellent performance in suppressing the graft rejection after transplantation of the organs, such as kidney, liver, heart, pancreas, etc., and are attracting increased attention. Namely, Cyclosporine and other immunosuppressive drugs, which can reduce outstandingly the incidence of acute rejection after organ transplantation and find frequent application in organ transplantation, lower the incidence of bone marrow depression, and can offer the advantage that severe infections brought about by a reduced number of leucocytes can be prevented from developing to thereby facilitate the rejection management after organ transplantation to be conducted, thus enabling the survival performance of organ transplantation to be enhanced remarkably. However, such immunosuppressive drugs, Cyclosproin, etc., are also observed to produce side effects or adverse reactions, which include those occurring at sites other than the site of transplantation or systemic ones, such as nephrotoxicity, hepatotoxicity, neuropathy, hypertension, necrosis of caput femoris, cataract, diabetes mellitus, acute pancreatitis, cytomegalovirus infections, etc. It is known that HGH is able to alleviate such systemic side effects caused by the immunosuppressive drugs (refer to the Official Gazette of JP Hei 08-89869 A). HGF is the protein which was discovered by the present inventors, Nakamura et al., to be present in the sera of the regenerated liver of rats with regenerating liver and found to act as a factor capable of proliferating mature hepatocytes in vitro (refer to Biochemical and Biophysical Research Communications, 1984, vol. 122, p. 1450-1459). Furthermore, Nakamura et al. succeeded in isolating HGF from platelets of a rat (refer to Proc. Nat. Acad. Sci., 1986, vol. 83, p. 6489, and FEBS Letters, 1987, vol. 22, p. 311), and identified partly its amino acid sequence. Subsequently, Nakamura et al. conducted cDNA cloning of human and rat HGF on the basis of the amino acid sequence elucidated, and succeeded in producing HGF in the form of a protein through introduction of the resultant cDNA into animal cells by recombinant DNA technology (for example, refer to Nature, 1989, vol. 342, p. 440-443).